Computation of Balanced Realisation Approximations of Delay Systems

This paper presents numerical algorithms for the construction of finite dimensional balanced approximations of delay systems of the form e −sT g(s) where g(s) is scalar, rational and strictly proper. The Hankel singular values are obtained as the zero crossings of a determinant function in which matrix transformations and scaling are introduced for reducing the propagation of numerical errors. The mesh for searching Hankel singular values is made efficient through the use of an asymptotic formula. Numerical examples are used to illustrate the approximation method.

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